A New Class of Private Chi-Square Tests
This work addresses privacy-preserving statistical testing for data analysts, but it is incremental as it builds on prior private testing methods.
The authors tackled the problem of private hypothesis testing by developing new test statistics that match the asymptotic distributions of classical chi-square tests after adding privacy noise, and empirically showed these outperform prior methods that used noisy versions of existing statistics.
In this paper, we develop new test statistics for private hypothesis testing. These statistics are designed specifically so that their asymptotic distributions, after accounting for noise added for privacy concerns, match the asymptotics of the classical (non-private) chi-square tests for testing if the multinomial data parameters lie in lower dimensional manifolds (examples include goodness of fit and independence testing). Empirically, these new test statistics outperform prior work, which focused on noisy versions of existing statistics.